Sequences and Series Review

Front

What does a1 represent?

Back

First term

Front

Evaluate the arithmetic series: \(\sum_{n=1}^{10}(7n-2)\).

Back

365

Front

Find the 32nd term of this sequence: 9, 4, -1, -6, -11, ...

Back

-146

Front

Find a26 in the arithmetic sequence: -15, -35, -55, -75, ...

Back

-515

Front

Evaluate the infinite geometric series: 3 - 2 + \frac{4}{3} - \frac{8}{9} + ...

Back

\frac{9}{5}

Front

Define an arithmetic sequence.

Back

A sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by: \(a_n = a_1 + (n-1)d\), where \(d\) is the common difference.

Front

What is a geometric series?

Back

A series where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the formula for the sum of the first n terms of an arithmetic series?

Back

The sum is given by: \(S_n = \frac{n}{2}(a_1 + a_n)\) or \(S_n = \frac{n}{2}(2a_1 + (n-1)d)\).

Front

How do you find the common difference in an arithmetic sequence?

Back

Subtract the first term from the second term: \(d = a_2 - a_1\).